Deriving gravitational potential energy from work against gravity

Steps:

• Gravitational potential energy change ΔE equals work done to lift object against gravity over height Δh.
• Work done = force × distance, where distance is Δh.
• Force required equals object's weight.
• Weight = mass × g, so work = mgΔh, yielding ΔE = mgΔh.

Why C is correct:

• Weight = mg provides the gravitational force in the work calculation, directly substituting into work = force × Δh for ΔE.

Why the others are wrong:

• A: Kinetic energy formula unrelated to potential energy derivation.
• B: Work = force × distance is used but insufficient alone without defining force as weight.
• D: Power × time defines work indirectly, not core to potential energy setup.

Final answer: C